This open-label, multicenter, non-randomized study will provide continued access to vemurafenib for eligible participants with BRAF V600 mutation-positive malignancy, who were previously enrolled and treated in an antecedent vemurafenib protocol and did not meet the protocol's criteria for disease progression, or are treated beyond progression and are still deriving clinical benefit (as assessed by investigator), and may therefore potentially benefit from continued treatment with vemurafenib. Participants will receive treatment with oral vemurafenib at 960 milligrams (mg) twice daily (BID), 720 mg BID, or 480 mg BID, depending on the last dose in the antecedent protocol. Treatment will continue until progression of disease or as long as the participant is deriving clinical benefit, as judged by the investigator (case-by-case decision with approval of the Medical Monitor), death, withdrawal of consent, unacceptable toxicity, loss to follow-up, or decision of the Sponsor to terminate the study, whichever occurs first.